Pion-nucleon scattering relations at next-to-leading order in 1/N _c

We obtain relations between partial-wave amplitudes for πN → πN and πN → πΔ directly from large N_c QCD. While linear relations among certain amplitudes holding at leading order (LO) in 1/N _c were derived in the context of chiral soliton models two decades ago, the present work employs a fully model-independent framework based on consistency with the large N_c expansion. At LO in 1/N_c we reproduce the soliton model results; however, this method allows for systematic corrections. At next-to-leading order (NLO), most relations require additional unknown functions beyond those appearing at LO and thus have little additional predictive power. However, three NLO relations for the πN → πΔ reaction are independent of unknown functions and make predictions accurate at this order. The amplitudes relevant to two of these relations were previously extracted from experiment These relations describe experiment dramatically better than their LO counterparts.